Unlike plate capacitors where 2 plates are used to form a capacitor, cylindrical capacitors are made by using two concentric cylindrical shells or wires and these two cylinders and wires are separated by using a dielectric medium.
Only difference between plate capacitor and cylindrical capacitor is its shape.
Electrical cable is best example for cylindrical capacitors.
How to calculate capacitance of a Cylindrical capacitor:-
For Calculating capacitance of a cylindrical capacitor let’s take radius of inner cylinder as r1 and outer cylinder as r2. Now let’s take permittivity of dielectric material used to form capacitor as εa.
As in case of plate capacitor where one plate is acts cathode and other acts as an anode now in similar case let’s take inner cylinder charge per meter length on outer surface of inner cylinder as +q and similarly on inner surface of outer cylinder as –q coulombs.
In practical +q charge is considered to be on axis and outer circle is earthed so that person touching the capacitor doesn’t get the shock.
Now for calculating capacitance of capacitor:-
Surface area of the coaxial cylinder = 2
x= Radius of cylinder a meter and
Length =1 meter
Now electrical field intensity at “x” meter away from center of inner cylinder is as below:-
Ex = Q Volt/Meter
Where εo= Permittivity of vacuum or permittivity of free space, its value is 8.84 x 10-12 Farad/meter
Potential difference between two plates or two cylinders is as below:-
So more will be the length of capacitor more will be the capacitance.
Capacitor is also known as condenser.